Question: $f(x) = \sqrt{ 2 - \lvert x \rvert }$ What is the domain of the real-valued function $f(x)$ ?
Answer: $f(x)$ is undefined when the radicand (the expression under the radical) is less than zero. So we know that $2 - \lvert x \rvert \geq 0$ So $\lvert x \rvert \leq 2$ This means $x \leq 2$ and $x \geq -2$ ; or, equivalently, $-2 \leq x \leq 2$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid -2\leq x \leq2\, \}$.